Principle of Virtual Work and the forces that DO NOT do work

[Trying2Learn]

TL;DR Summary

How do you get the reaction forces that do no work

In this 2D figure below, I can place:

• a motor at O
• a motor at J
• gravity on each link

I can use Hamilton's principle, modified to the principle of virtual work and I can compute the motion of the linkage system.

I do not have to account for these force FOUR forces (in this planar problem):

1. 2 Reaction forces at O (they do no work)
2. 2 Reaction forces at J (they do no work)

I have no difficulty with the previous work, above... The next part, counfounds me, and I ask for help.

However, how would I find those four reaction forces that do no work?

Would I first have to solve the entire problem using PVW, get the velocity, acceleration, angular velocity and angular acceleration?

And then, return to free body diagrams, and with the kinematics and inertial terms (mass and moment of inertia), go back and mathematically deduce what those forces SHOULD be?

How does software do it?

I have never seen a textbook discuss this. They just blithely (sometimes smugly) pronounce the power of PVW as being able to ignore forces that do no work (which is true and wonderful), but they never present a systematic way to go back and get those other forces that do no work.UNLESS: they enter as constraints, brought in by Lagrange multipliers. If so, then I must research that, alone (before bothering any of you--you have all been patient). However, in the absence of having to use that formality, how would YOU solve for these reaction forces that do no work? Can someone start me off so that I can then teach myself the Lagrange multipliers?

 

[Trying2Learn]

I have changed my mind. This is a stupid question and the solution is simple. I am sorry for having wasted the time of some of you.

 

[Lnewqban]

This is a stupid question and the solution is simple.

Why?
What that simple solution would be?

 

[Trying2Learn]

Why?
What that simple solution would be?

Oh

THE FIRST PART: is that I use Principle of Virtual Work (PVW and calc.variations) and Generalized coordinates, and I find the angles and the motion. That was not my issue, though.

MY issue was now to get the reaction forces at the base, and between the two arms.

I was confused.

So I spent some time...

I cut the body up using Newton's third law (action and reaction) and get a series of equations for the support reaction forces and the interaction forces and I solved those, and I was done.

------------------------

I KNOW that it can ALSO be done by infusing the constraints directly with Lagrange multipliers, but I have never done that before.

What irritated me, is that most books just blithely state "we can solve for the motion by PVW since the reaction forces can be ignored (they do not work); but no book (at least the ones I have seen), takes the next step and shows you (Either by Free body Diagrams or Lagrange Multipliers) how to get the reactions.

 

[Lnewqban]

I see.
Thank you very much, @Trying2Learn